Modelling Water Flow in Trees and Soil Root Zone Based on 3D Plant Architecture.

We apply a functional-structural model of tree water flow to single old-growth trees of a temperate broad-leaved forest stand. Roots, stems and branches are represented by connected porous cylinder elements that are divided into the inner heartwood cylinders surrounded by xylem and phloem.

Xylem water flow is simulated by applying a non-linear Darcy water flow in porous media driven by the water potential gradient according to the cohesion-tension theory. The flow model is based on physiological input parameters such as the hydraulic conductivity, stomatal response to leaf water potential and root water uptake capability and, thus, can reflect the different properties of tree species.

Actual root water uptake is calculated using a Darcy law based on the gradient between root xylem water potential and rhizosphere soil water potential and by simulation of soil water flow using Richards equation.

A leaf stomatal conductance model is combined with the hydrological tree and soil water flow model and a spatially explicit three-dimensional canopy light model. The structure of the canopy and the tree architectures are derived by applying an automatic tree skeleton extraction algorithm from point clouds obtained by applying a terrestrial laser scanner allowing an explicit representation of the water flow path in the stem and branches. The high spatial resolution of the root and branch geometry and connectivity makes the detailed modelling of the water use of single trees possible and allows for the analysis of the interaction between single trees and the influence of the canopy light regime on the water flow inside the xylem.

The model can be applied at various sites and  to different tree species, allowing the up-scaling of the water usage of single trees to the total transpiration of mixed stands.

Examples are given to reveal differences between diffuse- and ring-porous tree species and to simulate the diurnal dynamics of transpiration, stem sap flux, and  root water uptake observed during the vegetation period at different sites.